posts

posts/ats.md

@@ -3,6 +3,8 @@ title: a little ats program
 date: 2022-09-16
 tags: [computer, ATS, cool languages]
 show-toc: true
+summary: |
+  a little program in a little-known, little-documented language called ATS.
 ...
 
 [ats] is a language that is a little infamous among type system likers, for its
@@ -60,9 +62,7 @@ let's start by defining the syntax for types. it's going to be a single base
 type, and functions.
 
 $$
-\newcommand\Typ{\mathit{typ}}
-\newcommand\OR{\mathrel|}
-\Typ ::= \bullet \OR \Typ_1 \to \Typ_2
+A, B \operatorname{::=} \mathord• \mid A → B
 $$
 
 so obviously, my first attempt was to just write this:
@@ -159,11 +159,7 @@ overload print with print_typ
 types are done, now let's move on to terms. we just want names, lambdas, and
 application.
 
-$$
-\newcommand\Term{\mathit{term}}
-\newcommand\Var{\mathit{var}}
-\Term ::= \Var \OR \lambda \Var : \Typ. \Term \OR \Term_1 \; \Term_2
-$$
+$$ s, t \operatorname{::=} x \mid λ x : A. s \mid s \; t $$
 
 for the same reason as before, terms are indexed by their height, but _also_ by
 the number of variables in scope, since i want de bruijn indices to be